On the spectrum and structure constants of short operators in N=4 SYM at strong coupling

Abstract

We study short operators in planar $\mathcal{N}=4$ SYM at strong coupling, for general spin and $SO(6)$ symmetric traceless representations. At strong coupling their dimension grows like $\Delta \sim 2\sqrt{\delta }{\lambda }^{1/4}$ and their spectrum of degeneracies can be analysed by considering the massive spectrum of type II strings in flat space-time. We furthermore compute their structure constants with two arbitrary chiral primary operators. This is done by considering the four-point correlator of arbitrary chiral primary operators at strong coupling in planar $\mathcal{N}=4$ SYM, including the supergravity approximation plus the infinite tower of stringy corrections that contributes in the flat space limit. Our results are valid for generic rank $n$ symmetric traceless representations of $SO(6)$ and in particular for $n\gg 1$, as long as $n\ll {\lambda }^{1/4}$.

arXiv comment22 pages, v2: JHEP version

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• The type IIA Virasoro-Shapiro amplitude in AdS${}_4$ $\times$ CP${}^3$ from ABJM theory
• The Kaluza-Klein AdS Virasoro-Shapiro Amplitude near Flat Space